Today: Tim Cook and Marissa Mayer take the stage at San Francisco event, but Apple (AAPL) and Yahoo (YHOO) stock head in opposite directions. Also: Intel (INTC) is looking to push into the streaming-television market,

In this Wednesday, March 7, 2012 photo, Apple CEO Tim Cook announces the new iPad in San Francisco. Apple CEO Tim Cook is calling a shareholder lawsuit against the company a "silly sideshow, "on Tuesday, Feb. 12, 2013, even as he said he is open to looking at the shareholder's proposals for sharing more cash with investors. (AP Photo/Paul Sakuma, File)

The high-profile heads of Apple and Yahoo took the stage at a San Francisco conference to spread the gospel of their Silicon Valley tech companies Tuesday, but stock in the two companies headed in opposite directions on Wall Street.

Apple CEO Tim Cook took his turn at the podium first Tuesday morning, speaking early enough that he could still catch a flight to Washington D.C. to accompany first lady Michelle Obama at the president's State of the Union address in the evening. Cook's speech did not break any new ground for Apple, with the CEO declining to verify that the company will launch a cheaper iPhone, though he did point out that iPods eventually received a much wider range of prices.

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The most newsworthy statements Cook made related to the most recent drama Apple has encountered, a lawsuit from activist investor David Einhorn, who heads hedge fund Greenlight Capital and wants Apple to return some of its $137 billion in cash to shareholders.

Cook called the lawsuit, which seeks to block a shareholder vote on a proposal involving issuance of preferred shares, "a silly sideshow."

"Now, we do have some cash," Cook said, "but it's a privilege to be in this position. Last quarter, cash flow from operations for Apple was over $23 billion. It's an incredible privilege for us to be in this position that we can seriously consider returning additional cash to shareholders."

The speech, at a conference sponsored by one of the largest investment banks in the United States, was seen by many as a chance for Cook to reassure investors that Apple is headed in the right direction and will pull out of the tailspin its share price has suffered in the past five months.

"I see a market that is incredible to be in -- maybe the best market of all times," Cook told the conference. "Apple has enormous momentum."

That momentum wasn't apparent on Wall Street, where Apple's recent rebound ended with a 2.5 percent drop Tuesday, when shares closed at $467.84. Weakness may have its roots away from Cook's speech, however: Citi analysts issued a note Tuesday morning doubting Apple's ability to turn around its diminishing dominance of the tablet market.

"After analyzing the data, we have new concerns about the health of the 10-inch tablet market and, absent any material innovations (we do not count a Retina Mini or lighter/thinner iPad 5 among these), we remain concerned about Apple's ability to maintain market share," the note read.

Yahoo, which is quite used to analysts' doubts and a wilting stock price, has been enjoying a renaissance of sorts in the past few months, which continued Tuesday with a second consecutive day of reaching five-year highs. Wall Street's revived hopes for Yahoo mostly rest on the shoulders of its CEO, Marissa Mayer, who is looking to mobile for the future of Yahoo.

In her talk Tuesday, Mayer said her vision for the company actually includes fewer mobile apps than the dozens her company offers now, with hopes that she will be able to cut the number of app offerings down to "the dozen or so applications that people use all the time on their phone."

One of the most-used apps on mobile devices is Facebook, and Mayer hopes that her company can foster a closer relationship with the Menlo Park social network, she said Tuesday.

"A lot of the strengths of Facebook are available to Yahoo users. That's something we want to build upon. We have a real commitment to bringing valuable content to our users," she said.

Mayer isn't all talk when it comes to mobile: On Tuesday, her company announced its third acquisition in the mobile sector in four months, acquiring Alike, an app that offers recommendations for restaurants and other nearby offerings based on a user's previously stated preferences.

The deal, which has an undisclosed price tag, seems to indicate Yahoo will focus on finding local offerings -- which Mayer worked on at Google (GOOG) -- as part of its mobile strategy, though Alike's founder has said the most important part of its efforts have been in "Big Data."

Yahoo stock rose as high as $21.40 before closing with a 1.5 percent gain at $21.21 -- prices that are the highest for Yahoo intraday and closing trades since 2008.

Intel plans to launch set-top box, but analysts doubtful

At a separate conference, Intel confirmed that it is pushing into the streaming-television market, a costly gambit in a crowded sector that could pay off if the Santa Clara chipmaker manages to crack the code.

Erik Huggers, who leads Intel Media, told an AllThingsD conference in Dana Point that his company is seeking to develop and market a set-top box that will deliver live and on-demand content over the Internet, with hopes for a 2013 launch. The device even includes a camera that will identify and watch the viewer, allowing for targeted ads and content.

"We're actively testing it in the field with employees. It's not the final product, but it's certainly functional," Huggers said.

An over-the-Web offering that offers more bundling options at a lower price than cable is a dream for many of Silicon Valley's biggest names, with Netflix coming the closest to succeeding so far. Apple and Google have both introduced TV products, but neither has gone very far, as content providers shy away from non-cable offerings; Intel did not say it has signed any deals with content providers.

With so many companies ahead of Intel in the effort, and pushback from the companies that would have to sign on to make Intel's set-top box viable, analysts and insiders were wary.

"The chance that Intel launches is zero," Bernard Gershon, head of a consultant group called GershonMedia that advises media and digital executives, told Reuters. "They haven't cut any deals with any content companies, and they are not offering something that differentiates itself enough on service or price to get the deals done."

Intel stock gained 0.8 percent on the day to close at $21.19.

Social-networking weakness hurts tech stocks, but solar keeps rising

Wall Street gained slightly as a whole on Tuesday, with the Dow Jones closing near all-time highs, but tech stocks were some of the weakest performers, with the tech-heavy Nasdaq the only major U.S. stock index to fall on the day. The SV150 index of Silicon Valley's largest tech firms fell harder, declining 0.6 percent as social-networking stocks took a hit.

Facebook declined 3.2 percent on the day to $27.37 and has now fallen more than 11 percent in the month of February amid louder doubts about its mobile business. Two analysts chopped their ratings on the company Tuesday, with mobile the focus of both.

"The pace at which (Facebook's mobile gains" have evolved over the last two quarters justifies some caution," Bernstein Research analyst Carlos Kirjner wrote; he cut Facebook from "Outperform," similar to "Buy," to his equivalent of "Hold."

BTIG actually dropped Facebook to a "Sell" rating with a $22 price target, explaining in a note, "We struggle to believe Facebook can continue to ramp the ad load on mobile the way they did in" the fourth quarter.

Former close Facebook partner Zynga also experienced weakness Tuesday, dropping 11.7 percent after a strong run of gains on the back of a surprise fourth-quarter profit and positive signs on the future of online gambling. LinkedIn's strong run following its earnings report also came to an end, as the Mountain View company gave back 0.3 percent on the day.

While social networking was weak, solar stocks continued to run hot. San Jose-based SunPower (SPWRA) reached a 52-week high of $10.15 in Tuesday trading before closing at $9.71, a gain of 2.9 percent. San Mateo installer SolarCity hit new highs for the second consecutive day after a Monday report vindicated its business model; shares moved as high as $18.32 before closing with a 9.1 percent gain at $18.18. SolarCity Chairman Elon Musk took a loss at his other company, however, as Tesla shares dropped another 1.4 percent after Monday's drama.

And the widely watched Standard & Poor's 500 index: Up 2.42, or 0.16 percent, to 1,519.43

Check in weekday afternoons for the 60-Second Business Break, a summary of news from Mercury News staff writers, The Associated Press, Bloomberg News and other wire services. Contact Jeremy C. Owens at 408-920-5876; follow him at Twitter.com/mercbizbreak.